Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Chapter R.5, Problem 8E
To determine
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- Suppose that you have the differential equation:
dy
= (y - 2) (y+3)
dx
a. What are the equilibrium solutions for the differential equation?
b. Where is the differential equation increasing or decreasing? Show how you know.
Showing them on the drawing is not enough.
c. Where are the changes in concavity for the differential equation? Show how you
know. Showing them on the drawing is not enough.
d. Consider the slope field for the differential equation. Draw solution curves given the
following initial conditions:
i. y(0) = -5
ii. y(0) = -1
iii. y(0) = 2
5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force
of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass
is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I
purposefully removed the units- don't worry about them. Assume no conversions are
needed.)
a) Find the equation for the displacement of the spring mass at time t.
b) Write the equation for the displacement of the spring mass in phase-mode form.
c) Characterize the damping of the spring mass system as overdamped, underdamped or
critically damped. Explain how you know.
D.E. for Spring Mass Systems
k
m* g = kLo
y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo
m
2
A₁ = √c₁² + C₂²
Q = tan-1
4. Given the following information determine the appropriate trial solution to find yp. Do not
solve the differential equation. Do not find the constants.
a) (D-4)2(D+ 2)y = 4e-2x
b) (D+ 1)(D² + 10D +34)y = 2e-5x cos 3x
Chapter R Solutions
Calculus For The Life Sciences
Ch. R.1 - YOUR TURN 1 Perform the operation...Ch. R.1 - YOUR TURN 2 Perform the operation (3y+2)(4y22y5).Ch. R.1 - Prob. 1ECh. R.1 - Prob. 2ECh. R.1 - Prob. 3ECh. R.1 - Prob. 4ECh. R.1 - Prob. 5ECh. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations. 9m(2m2+3m1)Ch. R.1 - Prob. 8E
Ch. R.1 - Prob. 9ECh. R.1 - Prob. 10ECh. R.1 - Perform the indicated operations. (23x)(2+3x)Ch. R.1 - Prob. 12ECh. R.1 - Prob. 13ECh. R.1 - Perform the indicated operations....Ch. R.1 - Prob. 15ECh. R.1 - Prob. 16ECh. R.1 - Prob. 17ECh. R.1 - Prob. 18ECh. R.1 - Prob. 19ECh. R.1 - Perform the indicated operations. (r+2s3t)(2r2s+t)Ch. R.1 - Prob. 21ECh. R.1 - Prob. 22ECh. R.1 - Prob. 23ECh. R.1 - Prob. 24ECh. R.1 - Prob. 25ECh. R.1 - Prob. 26ECh. R.2 - YOUR TURN 1 Factor 4z4+4z3+18z2.Ch. R.2 - Prob. 2YTCh. R.2 - Prob. 1ECh. R.2 - Prob. 2ECh. R.2 - Prob. 3ECh. R.2 - Prob. 4ECh. R.2 - Prob. 5ECh. R.2 - Prob. 6ECh. R.2 - Prob. 7ECh. R.2 - Prob. 8ECh. R.2 - Prob. 9ECh. R.2 - Prob. 10ECh. R.2 - Prob. 11ECh. R.2 - Factor each polynomial. If a polynomial cannot be...Ch. R.2 - Prob. 13ECh. R.2 - Prob. 14ECh. R.2 - Prob. 15ECh. R.2 - Prob. 16ECh. R.2 - Prob. 17ECh. R.2 - Prob. 18ECh. R.2 - Prob. 19ECh. R.2 - Prob. 20ECh. R.2 - Prob. 21ECh. R.2 - Prob. 22ECh. R.2 - Prob. 23ECh. R.2 - Prob. 24ECh. R.2 - Prob. 25ECh. R.2 - Prob. 26ECh. R.2 - Prob. 27ECh. R.2 - Prob. 28ECh. R.2 - Prob. 29ECh. R.2 - Factor each polynomial. If a polynomial cannot be...Ch. R.2 - Prob. 31ECh. R.2 - Prob. 32ECh. R.3 - YOUR TURN 1 Write in lowest terms. z2+5z+62z2+7z+3Ch. R.3 - Prob. 2YTCh. R.3 - Prob. 1ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 3ECh. R.3 - Prob. 4ECh. R.3 - Prob. 5ECh. R.3 - Prob. 6ECh. R.3 - Prob. 7ECh. R.3 - Prob. 8ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 10ECh. R.3 - Prob. 11ECh. R.3 - Prob. 12ECh. R.3 - Prob. 13ECh. R.3 - Prob. 14ECh. R.3 - Prob. 15ECh. R.3 - Prob. 16ECh. R.3 - Prob. 17ECh. R.3 - Prob. 18ECh. R.3 - Prob. 19ECh. R.3 - Prob. 20ECh. R.3 - Prob. 21ECh. R.3 - Prob. 22ECh. R.3 - Prob. 23ECh. R.3 - Prob. 24ECh. R.3 - Prob. 25ECh. R.3 - Prob. 26ECh. R.3 - Prob. 27ECh. R.3 - Prob. 28ECh. R.3 - Prob. 29ECh. R.3 - Prob. 30ECh. R.3 - Prob. 31ECh. R.3 - Prob. 32ECh. R.3 - Prob. 33ECh. R.3 - Prob. 34ECh. R.3 - Prob. 35ECh. R.3 - Prob. 36ECh. R.3 - Prob. 37ECh. R.3 - Prob. 38ECh. R.4 - YOUR TURN 1 Solve 3x7=4(5x+2)7x.Ch. R.4 - Prob. 2YTCh. R.4 - Prob. 3YTCh. R.4 - Prob. 4YTCh. R.4 - Prob. 1ECh. R.4 - Prob. 2ECh. R.4 - Prob. 3ECh. R.4 - Prob. 4ECh. R.4 - Prob. 5ECh. R.4 - Prob. 6ECh. R.4 - Prob. 7ECh. R.4 - Solve each equation 4[2p(3p)+5]=7p2Ch. R.4 - Prob. 9ECh. R.4 - Prob. 10ECh. R.4 - Prob. 11ECh. R.4 - Prob. 12ECh. R.4 - Prob. 13ECh. R.4 - Prob. 14ECh. R.4 - Prob. 15ECh. R.4 - Prob. 16ECh. R.4 - Prob. 17ECh. R.4 - Prob. 18ECh. R.4 - Prob. 19ECh. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Prob. 21ECh. R.4 - Prob. 22ECh. R.4 - Prob. 23ECh. R.4 - Prob. 24ECh. R.4 - Prob. 25ECh. R.4 - Prob. 26ECh. R.4 - Prob. 27ECh. R.4 - Prob. 28ECh. R.4 - Prob. 29ECh. R.4 - Prob. 30ECh. R.4 - Prob. 31ECh. R.4 - Prob. 32ECh. R.4 - Prob. 33ECh. R.4 - Prob. 34ECh. R.4 - Prob. 35ECh. R.4 - Prob. 36ECh. R.4 - Prob. 37ECh. R.5 - YOUR TURN Solve 3z25z+7.Ch. R.5 - Prob. 2YTCh. R.5 - Prob. 3YTCh. R.5 - Prob. 1ECh. R.5 - Prob. 2ECh. R.5 - Prob. 3ECh. R.5 - Prob. 4ECh. R.5 - Prob. 5ECh. R.5 - Prob. 6ECh. R.5 - Prob. 7ECh. R.5 - Prob. 8ECh. R.5 - Prob. 9ECh. R.5 - Prob. 10ECh. R.5 - Prob. 11ECh. R.5 - Prob. 12ECh. R.5 - Prob. 13ECh. R.5 - Prob. 14ECh. R.5 - Prob. 15ECh. R.5 - Prob. 16ECh. R.5 - Prob. 17ECh. R.5 - Prob. 18ECh. R.5 - Prob. 19ECh. R.5 - Prob. 20ECh. R.5 - Prob. 21ECh. R.5 - Solve each inequality and graph the solution....Ch. R.5 - Prob. 23ECh. R.5 - Prob. 24ECh. R.5 - Prob. 25ECh. R.5 - Prob. 26ECh. R.5 - Prob. 27ECh. R.5 - Prob. 28ECh. R.5 - Prob. 29ECh. R.5 - Prob. 30ECh. R.5 - Prob. 31ECh. R.5 - Prob. 32ECh. R.5 - Prob. 33ECh. R.5 - Prob. 34ECh. R.5 - Prob. 35ECh. R.5 - Prob. 36ECh. R.5 - Prob. 37ECh. R.5 - Prob. 38ECh. R.5 - Prob. 39ECh. R.5 - Prob. 40ECh. R.5 - Prob. 41ECh. R.5 - Prob. 42ECh. R.5 - Solve each inequality. m3m+50Ch. R.5 - Prob. 44ECh. R.5 - Prob. 45ECh. R.5 - Prob. 46ECh. R.5 - Prob. 47ECh. R.5 - Prob. 48ECh. R.5 - Prob. 49ECh. R.5 - Prob. 50ECh. R.5 - Prob. 51ECh. R.5 - Prob. 52ECh. R.5 - Prob. 53ECh. R.5 - Prob. 54ECh. R.6 - YOUR TURN 1 Simplify (y2z4y3z4)2.Ch. R.6 - YOUR TURN 2 Factor 5z1/3+4z2/3.Ch. R.6 - Evaluate each expression. Write all answers...Ch. R.6 - Prob. 2ECh. R.6 - Prob. 3ECh. R.6 - Prob. 4ECh. R.6 - Prob. 5ECh. R.6 - Prob. 6ECh. R.6 - Prob. 7ECh. R.6 - Prob. 8ECh. R.6 - Prob. 9ECh. R.6 - Prob. 10ECh. R.6 - Prob. 11ECh. R.6 - Simplify each expression. Assume that all...Ch. R.6 - Prob. 13ECh. R.6 - Prob. 14ECh. R.6 - Prob. 15ECh. R.6 - Prob. 16ECh. R.6 - Prob. 17ECh. R.6 - Prob. 18ECh. R.6 - Prob. 19ECh. R.6 - Prob. 20ECh. R.6 - Prob. 21ECh. R.6 - Prob. 22ECh. R.6 - Prob. 23ECh. R.6 - Simplify each expression, writing the answer as a...Ch. R.6 - Prob. 25ECh. R.6 - Simplify each expression, writing the answer as a...Ch. R.6 - Prob. 27ECh. R.6 - Prob. 28ECh. R.6 - Prob. 29ECh. R.6 - Prob. 30ECh. R.6 - Prob. 31ECh. R.6 - Prob. 32ECh. R.6 - Prob. 33ECh. R.6 - Prob. 34ECh. R.6 - Prob. 35ECh. R.6 - Prob. 36ECh. R.6 - Prob. 37ECh. R.6 - Prob. 38ECh. R.6 - Prob. 39ECh. R.6 - Prob. 40ECh. R.6 - Prob. 41ECh. R.6 - Prob. 42ECh. R.6 - Prob. 43ECh. R.6 - Prob. 44ECh. R.6 - Prob. 45ECh. R.6 - Prob. 46ECh. R.6 - Prob. 47ECh. R.6 - Prob. 48ECh. R.6 - Prob. 49ECh. R.6 - Prob. 50ECh. R.6 - Prob. 51ECh. R.6 - Prob. 52ECh. R.6 - Prob. 53ECh. R.6 - Prob. 54ECh. R.6 - Prob. 55ECh. R.6 - Prob. 56ECh. R.7 - YOUR TURN Simplify 28x9y5.Ch. R.7 - Prob. 2YTCh. R.7 - Prob. 1ECh. R.7 - Prob. 2ECh. R.7 - Prob. 3ECh. R.7 - Prob. 4ECh. R.7 - Prob. 5ECh. R.7 - Prob. 6ECh. R.7 - Prob. 7ECh. R.7 - Prob. 8ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 10ECh. R.7 - Prob. 11ECh. R.7 - Prob. 12ECh. R.7 - Prob. 13ECh. R.7 - Prob. 14ECh. R.7 - Prob. 15ECh. R.7 - Prob. 16ECh. R.7 - Prob. 17ECh. R.7 - Prob. 18ECh. R.7 - Prob. 19ECh. R.7 - Prob. 20ECh. R.7 - Prob. 21ECh. R.7 - Prob. 22ECh. R.7 - Prob. 23ECh. R.7 - Prob. 24ECh. R.7 - Prob. 25ECh. R.7 - Prob. 26ECh. R.7 - Prob. 27ECh. R.7 - Prob. 28ECh. R.7 - Prob. 29ECh. R.7 - Prob. 30ECh. R.7 - Prob. 31ECh. R.7 - Prob. 32ECh. R.7 - Prob. 33ECh. R.7 - Prob. 34ECh. R.7 - Prob. 35ECh. R.7 - Prob. 36ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 38ECh. R.7 - Prob. 39ECh. R.7 - Prob. 40ECh. R.7 - Rationalize each numerator. Assume that all...Ch. R.7 - Rationalize each numerator. Assume that all...Ch. R.7 - Rationalize each numerator. Assume that all...Ch. R.7 - Prob. 44E
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